SOLUTION: These problems are froma a sample final, not a text book. question #1 - 9^2x = 5^3x-4 solve equation question #2 - log(base 5)e - use change of base formula question #3 - l

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: These problems are froma a sample final, not a text book. question #1 - 9^2x = 5^3x-4 solve equation question #2 - log(base 5)e - use change of base formula question #3 - l      Log On

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Question 139875: These problems are froma a sample final, not a text book.
question #1 - 9^2x = 5^3x-4 solve equation
question #2 - log(base 5)e - use change of base formula
question #3 - log (base 2)(a^2 sqrt b^3)^4 write as summ/differ of log,express powers as factors
question #4 - ln(9-x^2) - find domain
I am studying my sample final...finals coming soon, these 4 problems are giving me trouble...ANY HELP WOULD BE GREATLY APPRECIATED!!!!
exponetial and logaarithmic problems are giving me major pproblems.
Thanks again for all your help!!!
Answer by stanbon(48569) About Me  (Show Source):
You can put this solution on YOUR website!
question #1 - 9^(2x) = 5^(3x-4) solve equation
Take the log of both sides:
2xlog9 = (3x-4)log5
xlog81 = 3xlog5 -4log5
xlog81 = xlog15^3 - log5^4
x(log81-log15^3) = log5^4
x = log5^4/(log81 -log15^3)
x = -1.7261
--------------------------
question #2 - log(base 5)e - use change of base formula
log5 e = lne/ln5 = 1/ln5 = 0.62133...
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question #3 - log (base 2)(a^2 sqrt b^3)^4 write as summ/differ of log,express powers as factors:
log (base 2)(a^2 sqrt b^3)^4 = log2 (a^8 b^2)= 8log2 a + 2log2 b
---------------------------------
question #4 - ln(9-x^2) - find domain
9-x^2 > 0
x^2 < 9
-3 < x < 3
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Domain: All Real numbers except -3 < x < 3
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Cheers,
Stan H.